4-regular partitions and the pod function

The function pod(n) enumerates the partitions of n wherein odd parts are distinct and even unrestricted. Recently, a number properties for have been established. In this paper, we use connections with 4-regular and, fixed k ∈ {0, 2}, into not congruent to modulo 4 in order obtain new pod(n). context, derive two infinite families linear inequalities involving We also identities Watson type.